Question: Reduce to lowest terms: $ \dfrac{5}{2} \div \dfrac{9}{5} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{9}{5}$ is $ \dfrac{5}{9}$ Therefore: $ \dfrac{5}{2} \div \dfrac{9}{5} = \dfrac{5}{2} \times \dfrac{5}{9} $ $ \phantom{ \dfrac{5}{2} \times \dfrac{5}{9}} = \dfrac{5 \times 5}{2 \times 9} $ $ \phantom{ \dfrac{5}{2} \times \dfrac{5}{9}} = \dfrac{25}{18} $